Oscillator based complex coefficient adaptive notch filter and its applications

In this paper, a new complex adaptive notch filter using the oscillator based algorithm has been proposed. The approach presented for second-order real coefficient IIR filters has been applied to derive a coefficient-update algorithm for a first-order complex adaptive notch filter. The case where an input complex sinusoid is given by a sum of sequences with positive and negative frequencies has been considered. An analytical expression of a frequency estimation error due to sequence with negative frequency has been derived. Closed-form expression for frequency estimation mean square error dut to input noise is then derived. Analysis for frequency tracking error has been also presented for a complex linear chirp signal. Computer simulations show the effectiveness of the proposed algorithm.